NURBS自由曲面在光机设计和分析中的应用

周伟; 程德文; 许晨; 禹璐; 王庆丰; 王涌天; 金国藩

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NURBS自由曲面在光机设计和分析中的应用

周伟, 程德文, 许晨, 禹璐, 王庆丰, 王涌天, 金国藩

文章导航 > 红外与激光工程 > 2014 > 43(10): 3313-3320

周伟, 程德文, 许晨, 禹璐, 王庆丰, 王涌天, 金国藩. NURBS自由曲面在光机设计和分析中的应用[J]. 红外与激光工程, 2014, 43(10): 3313-3320.

引用本文:

周伟, 程德文, 许晨, 禹璐, 王庆丰, 王涌天, 金国藩. NURBS自由曲面在光机设计和分析中的应用[J]. 红外与激光工程, 2014, 43(10): 3313-3320.

Zhou Wei, Cheng Dewen, Xu Chen, Yu Lu, Wang Qingfeng, Wang Yongtian, Jin Guofan. Application of NURBS free-form surface in optomechanical design and analysis[J]. Infrared and Laser Engineering, 2014, 43(10): 3313-3320.

Citation:

Zhou Wei, Cheng Dewen, Xu Chen, Yu Lu, Wang Qingfeng, Wang Yongtian, Jin Guofan. Application of NURBS free-form surface in optomechanical design and analysis[J]. Infrared and Laser Engineering, 2014, 43(10): 3313-3320.

NURBS自由曲面在光机设计和分析中的应用

1.
北京理工大学光电学院,北京 100081;
2.
清华大学精密测试技术及仪器国家重点实验室,北京 100084

基金项目:

国家自然科学基金(61178038,61205024);国家基础研究计划(973)项目(2011CB706701);教育部新世纪优秀人才支持计划(NCET-12-0043)

详细信息

作者简介:
周伟(1988-),男,硕士生,主要从事光学设计方面的研究。Email:zw20070376@163.com

中图分类号: TP302.7

Application of NURBS free-form surface in optomechanical design and analysis

1.
School of Optoelectronics,Beijing Institute of Technology,Beijing 100081,China;
2.
State Key Laboratory of Precision Measurement Technology and Instrument,Tsinghua University,Beijing 100084,China

摘要: 针对光学曲面要求面形描述能力和拟合精度高以及光线追迹速度快的要求,研究了NURBS作为自由曲面的拟合、坐标空间转换和光线追迹算法。首先使用多分辨率B样条拟合方法浅度非球面,深度非球面和Peaks自由曲面进行NURBS拟合,RMS误差均小于10 nm,表现出很好的适应性。其次研究了NURBS曲面的参数空间到坐标空间的转化算法,与传统曲面求导方法相比,速度提高了3倍以上。在提出合理迭代初值计算方法的基础上,将计算每个曲面点的时间缩短至0.3 ms。最后通过NURBS曲面在自由曲面头盔系统的光机分析中和CODEV用户自定义曲面中的成功运用,证明了NURBS曲面能很好地满足光机设计、分析和加工的要求。
- NURBS曲面 /
- 多分辨率B样条拟合 /
- 参数空间和坐标空间转化 /
- 光线追迹 /
- 光机分析
Abstract: Knowing that optical surface should have strong surface description and fitting ability and that ray-tracing speed of the surface should be fast, the fitting method and ray tracing algorithm of NURBS free-form surface were studied. Fitting mild slope asphere, deep slope asphere and peaks surface respectively to NURBS surface using Multilevel B-splines approximation(MBA), all of the fitting residual errors were less than 10 nm, and it proved the NURBS surface is qualified for various free-form surface. Several high-precision and fast methods for inversion of NURBS surface were studied, and the ray tracing algorithm's speed was 3 times faster than traditional derivative algorithm. Given an appropriate iterative initial value, the time for calculating each point could be minimized to 0.3 ms. Examples of successfully using NURBS surface in optomechanical analysis of free-form surface prism system and in CODEV user-defined surface, show that the NURBS surface is fully adequate in optomechanical design, analysis and fabrication.
- NURBS surface /
- multilevel B-splines approximation(MBA) /
- coordinate inversion /
- ray trace /
- optomechanical analysis

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NURBS自由曲面在光机设计和分析中的应用

1. 北京理工大学光电学院,北京 100081;

2. 清华大学精密测试技术及仪器国家重点实验室,北京 100084

作者简介:
周伟(1988-),男,硕士生,主要从事光学设计方面的研究。Email:zw20070376@163.com

收稿日期: 2014-02-05
修回日期: 2014-03-03
刊出日期: 2014-10-25

基金项目:

国家自然科学基金(61178038,61205024);国家基础研究计划(973)项目(2011CB706701);教育部新世纪优秀人才支持计划(NCET-12-0043)

中图分类号: TP302.7

关键词:

摘要: 针对光学曲面要求面形描述能力和拟合精度高以及光线追迹速度快的要求,研究了NURBS作为自由曲面的拟合、坐标空间转换和光线追迹算法。首先使用多分辨率B样条拟合方法浅度非球面,深度非球面和Peaks自由曲面进行NURBS拟合,RMS误差均小于10 nm,表现出很好的适应性。其次研究了NURBS曲面的参数空间到坐标空间的转化算法,与传统曲面求导方法相比,速度提高了3倍以上。在提出合理迭代初值计算方法的基础上,将计算每个曲面点的时间缩短至0.3 ms。最后通过NURBS曲面在自由曲面头盔系统的光机分析中和CODEV用户自定义曲面中的成功运用,证明了NURBS曲面能很好地满足光机设计、分析和加工的要求。

English Abstract

Application of NURBS free-form surface in optomechanical design and analysis

1. School of Optoelectronics,Beijing Institute of Technology,Beijing 100081,China;

2. State Key Laboratory of Precision Measurement Technology and Instrument,Tsinghua University,Beijing 100084,China

Received Date: 2014-02-05
Rev Recd Date: 2014-03-03
Publish Date: 2014-10-25

Keywords:

NURBS surface /
multilevel B-splines approximation(MBA) /
coordinate inversion /
ray trace /
optomechanical analysis

Abstract: Knowing that optical surface should have strong surface description and fitting ability and that ray-tracing speed of the surface should be fast, the fitting method and ray tracing algorithm of NURBS free-form surface were studied. Fitting mild slope asphere, deep slope asphere and peaks surface respectively to NURBS surface using Multilevel B-splines approximation(MBA), all of the fitting residual errors were less than 10 nm, and it proved the NURBS surface is qualified for various free-form surface. Several high-precision and fast methods for inversion of NURBS surface were studied, and the ray tracing algorithm's speed was 3 times faster than traditional derivative algorithm. Given an appropriate iterative initial value, the time for calculating each point could be minimized to 0.3 ms. Examples of successfully using NURBS surface in optomechanical analysis of free-form surface prism system and in CODEV user-defined surface, show that the NURBS surface is fully adequate in optomechanical design, analysis and fabrication.